The related video inverse quantization technology will be explained by making a reference to FIG. 1. However, an attention should be paid to the fact that a quantizer E1001 is shown for a purpose of indicating an input/output relation with an element calculator E1002 for performing a video inverse quantization, namely to the fact that the video inverse quantization technology can be configured only of the element calculator E1002.
Further, it is assumed that one piece of a video frame having a gray scale with m vertical pixels and n horizontal pixels is a video signal vector x. However, the prior arts and the present invention are applicable for color video signals as well, as apparent from the explanation that will be later made. Further, the prior arts and the present invention are applicable even though the aforementioned video signal vector x is a sub-region of the video frame. Additionally, in this paper, “a set of a plurality of elements” and “an aggregation of a plurality of elements” are referred to as “a vector”.
The quantizer E1001 quantizes each elementxi,j(0≦i≦m−1,0≦j≦n−1)of the video signal vector x, and calculates a quantized value qi,j. Upon assuming the quantizer of E1001 to be a linear quantizer of which a quantization width is Qs,qi,j=floor(xi,j/Qs+0.5)  (1)is yielded. Where function floor( ), which is a floor function, is a function for returning a maximum integer, out of input values, being real number values. Hereafter, it is assumed that a set (an aggregation) of the aforementioned quantized values qi,j is a quantized value vector q.
The element calculator E1002 calculates an inverse-quantized value{circumflex over (x)}i,j by employing the aforementioned quantized value qi,j, and each element yi,j of another video signal vector y (auxiliary information y) having a correlation with the video signal vector x. Upon assuming a half-open interval corresponding to the aforementioned quantized value qi,j to be[Qi,j−,Qi,j+)(however,Qi,j−=Qs·qi,j−Qs/2,Qi,j+=Qs·qi,j+Qs/2)and a conditional provability density function corresponding to the aforementioned correlation to be fX|Y(x|y), the element calculator E1002 calculates each element (each inverse-quantized value){circumflex over (x)}i,j for which the minimum mean square error of the inverse-quantized video signal vector{circumflex over (x)},being the video signal vector that has been inverse-quantized, becomes minimized with the following conditional expectation value (FIG. 2).{circumflex over (x)}i,j=EX|y[x|xε[Qi,j−,Qi,j+),yi,j]=∫Qi,j−Qi,j+x·fX|y(x|yi,j)dx  (2)
Additionally, as a matter of fact, the approximate calculations (Non-patent literature 1, 2, and 3) that are replaced with the numerical expression (2) are utilized for the reason that a complete form of “conditional provability distribution fX|y is unknown”, and that “the calculation of the numerical expression (2) requires integral calculation”. For example, the Non-patent Literature 1 proposes to utilize the following numerical expression (2)′ instead of the numerical expression (2).
                                          x            ^                                i            ,            j                          =                  {                                                                                          Q                                          i                      ,                      j                                        -                                    ,                                                            y                                              i                        ,                        j                                                              <                                          Q                                              i                        ,                        j                                            -                                                                                                                                                                y                                          i                      ,                      j                                                        ,                                                            Q                                              i                        ,                        j                                            -                                        ≤                                          y                                              i                        ,                        j                                                              <                                          Q                                              i                        ,                        j                                            +                                                                                                                                                                Q                                          i                      ,                      j                                        +                                    ,                                                            Q                                              i                        ,                        j                                            +                                        ≤                                          y                                              i                        ,                        j                                                                                                                                                              (          2          )                '            
So long as the approximate calculations is exact, calculating the inverse-quantized values by utilizing the aforementioned auxiliary information y makes it possible to reduce the mean square error of the inverse-quantized video signal vector{circumflex over (x)}all the more as compared with the case of calculating the inverse-quantized values by simply inverse-quantizing the video signal vector.
The aforementioned video inverse quantization of the element calculator E1002 enables the inverse-quantized video signal vector{circumflex over (x)}of which the mean square error is smaller to be calculated.
Above, the explanation of the related arts is finished.